CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set B

Question. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is
(a) 11 cm
(b) 22 cm
(c) 27 cm
(d) 44 cm
Answer : B

Question. The angle described by a minute hand in 5 minutes is
(a) 30°
(b) 60°
(c) 90°
(d) None of these
Answer : A

Question. All the vertices of a rhombus lie on a circle. The area of the rhombus, if the area of the circle is 1256 cm² is [Use π = 3.14]
(a) 300 cm²
(b) 600 cm²
(c) 800 cm²
(d) 900 cm²
Answer : C

Question. The given figure is a sector of circle of radius 10.5 cm. The perimeter of the sector is [Take π = 7/22 ]

(a) 32 cm
(b) 44 cm
(c) 54 cm
(d) None of these
Answer : A

Question. In a circle of diameter 42 cm,if an arc subtends an angle of 60° at the centre where p = 22/7, then what will be the length of arc?
(a) 11 cm
(b) 20 cm
(c) 22 cm
(d) 28 cm
Answer : C

Question. A horse is tied to a pole with 28 m long rope. The perimeter of the field where the horse can graze is (Take π = 22/7)
(a) 60 cm
(b) 85 cm
(c) 124 cm
(d) 176 cm
Answer : D

Question. A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle 120°. The total area cleaned at each sweep of the blades is [Take π = 7/22]
(a) 360 cm²
(b) 448 cm²
(c) 556 cm²
(d) 924 cm²
Answer : D

Question. The difference of the areas of two segments of a circle formed by a chord of radius 5 cm subtending an angle of 90° at the centre is
(a) (25π/4 - 25/2)cm²
(b) (15π/4 - 7/2)cm²
(c) (7π/4 - 3/2)cm²
(d) None of these
Answer : A

Question. The area of the sector in the following figure showing a chord AB of a circle of radius 18 cm subtending an angle of 60° at the centre O is [Take π = 3.14]

(a) 151.31 cm²
(b) 169.56 cm²
(c) 173.33 cm²
(d) None of these
Answer : B

Question. An arc of length 15.7 cm subtends a right angle at the centre of the circle. Then the radius of the circle is
(a) 20 cm
(b) 10 cm
(c) 15 cm
(d) 12 cm
Answer : B

Question. A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. The radius of the circle is [Take π = 7/22]
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm
Answer : C

Question. The short and long hands of a clock are 4 cm and 6 cm long respectively. The sum of distances travelled by their tips in 2 days is
(a) 1148 cm
(b) 1426.35 cm
(c) 1910.85 cm
(d) None of these
Answer : C

Question. The area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm is
(a) 3.25 cm²
(b) 8.75 cm²
(c) 4.60 cm²
(d) 5.50 cm²
Answer : B

Question. The area of the shaded region in the given figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle is [Take π = 3.14]

(a) 128.56 cm²
(b) 145.33 cm²
(c) 248.16 cm²
(d) None of these
Answer : B

Question. The area of the largest circle that can be drawn inside the given rectangle of length ‘a’ cm and breadth ‘b’ cm (a > b) is
(a) (1/2)πb cm²
(b) (1/3)πb cm²
(c) (1/4)πb cm²
(d) πb2 cm²
Answer : C
 

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R).
Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): In a circle of radius 6 cm, the angle of a sector is 60°. Then the area of the sector is 18(6/7)cm².
Reason (R): Area of the circle with radius r is πr².
Answer : B

Question. Assertion (A): The length of the minute hand of a clock is 7 cm. Then the area swept by the minute hand in 5 minute is 12(5/6)cm².
Reason (R): The length of an arc of a sector of angle q and radius r is given by l = θ/360 x 2πr
Answer : B

1) A bicycle wheel makes 5000 revolution in moving 11 km. find the diameter of the wheel (d = 70 cm)

2) The radius of the wheel of a bus is 70cm, how many revolutions per minute must a wheel make in order to move at a speed

of 66 km/h (250)

3) A wheel has diameter 84cm. Find how many complete revolutions must it make to cover 792 metres (300)

4) In the figure o is the centre of a circle. The area of sector OAPB is 5/18 of the area of the circle. Find x

(100˚)

A B

p

5) Area of a sector of a circle is 1/6 to the area of circle. Find the degree measure of its minor arc (60˚)

6) Area of a sector of a circle of radius 14cm is 154 cm2 . Find the length of the corresponding arc of the sector (22 cm)

7) If the diameter of a semi circle protractor is 14 cm. Find its perimeter (36cm)

8) The circumference of a circle A is 132cm. It is equal to the sum of the circumference of two circles B & C, the radius of the circle

B is 14cm. Find the radius of circle C. (r = 7 cm)

9) The area of quadrant is 154sq cm. Find its perimeter. (50 cm)

10) Two circles touch externally. The sum of their areas is 130 Π sq.cm and the distance between their centres is 14cm. Find the radii of the Circles (11cm ,3cm)

11) Find the area of a quadrant of a circle whose circumference is 44cm (38.5cm2)

12) The perimeter of a sheet of paper in the shape of a quadrant of a circle is 75 cm. Find its area (346.5 sqcm)

13) A circular disc of 6cm radius is divided into 3 sectors with central angles 120˚, 150˚and 90˚.Find the ratio of the areas of 3 Sectors (4: 5: 3)

14) The difference between circumferences and diameter of a circle is 105 cm. Find the radius of the circle (24.5 cm)

15) Find the area of a major sector of a circle of diameter 42 cm and central angle is 60˚ (1155cm2)

16) If the area and circumference of a circle are numerically equal, then find the radius of the circle (2cm)

17) The length of a rope by which a cow is tethered is increased from 16m to 23m. How much additional area can the cow graze? Now (π =22/7) (2.38 Ѳm2)

18) What will be the increase in area of circle if its radius is increased by 40% (96%)

19) An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm2 . Find the radius of the circle (8cm)

20) The circumference of a circle exceeds the diameter by 16.8cm. Find the radius of circle (3.92cm)

21) The area enclosed between two concentric circles is 770 sq cm. If the radius of outer circle is 21cm. Find the radius of the inner circle. (14 cm)

22) The length of the minute hand of a clock is 7cm. How much area does it sweep in 20minutes (154/3 cm2)

23) The perimeter of a sector of a circle of radius 5.2cm is 16.4cm.Find the area of sector (15.6cm2)

24) Given a circle of radius 9cm, and the length of the chord AB of a circle is 9√3 cm, find the area of the sector formed by arc AB. (84. 85 cm2)

25) Length of minor arc of a circle of radius 10 cm is 14cm. Find the area of minor sector of a circle. (70cm2)

26) A chord 10 cm long is drawn in a circle of radius V50 cm. Find the area of minor segment (14. 285 cm2)

27) A chord AB of a circle of radius 14cm makes a right angle at the centre of the circle. Find the area of the minor segment. (π = 22/7) (56 cm2)

28) Find the area of the major segment APB, of a circle of radius 35 cm and ∟AOB = 90˚ (π = 22/7) P (3500 cm2) A B

29) A chord of a circle of radius 14cm subtends an angle of 120˚ at the centre Find the area of the corresponding minor segment of

The circle (π = 22/7, √3 = 1.73) (120.56 cm2 )

30) From a thin metallic piece, in the shape of a trapezium ABCD in which AB II CD and ∟BCD = 90˚, a quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2cm, calculate the area of the remaining (shaded) part of the metal sheet (π = 22/7) A B F (6.125 cm2)

Please click the below link to access CBSE Class 10 Mathematics Worksheet - Areas related to Circles (1)